信用风险模型.ppt

1、Issues in Credit Risk Modelling,Risk Management Symposium September 2, 2000,Bank of Thailand,Chotibhak Jotikasthira,天马行空官方博客： ；QQ:1318241189；QQ群：175569632,Bank of Thailand,Risk Management Symposium - September 2000,Page 2,Overview,BIS regulatory model Vs Credit risk models Current Issues in Credit R

2、isk Modelling Brief introduction to credit risk models Purpose of a credit risk model Common components Model from insurance (Credit Risk+) Credit Metrics KMV Model comparison,Bank of Thailand,Risk Management Symposium - September 2000,Page 3,BIS Regulatory Model Vs Credit Risk Models,BIS Risk-Based

3、 Capital Requirements All private-sector loans (uncollateralized) are subjected to an 8 percent capital reserve requirement, irrespective of the size of the loan, its maturity, and the credit quality of the borrowing counterparty. Note: Some adjustments are made to collateralized/guaranteed loans to

4、 OECD governments, banks, and securities dealers.,Bank of Thailand,Risk Management Symposium - September 2000,Page 4,Credit Risk Models - Credit Risk+ - Credit Metrics - KMV - Other similar models,BIS Regulatory Model Vs Credit Risk Models,天马行空官方博客： ；QQ:1318241189；QQ群：175569632,Bank of Thailand,Risk

5、 Management Symposium - September 2000,Page 5,Disadvantages of BIS Regulatory Model 1. Does not capture credit-quality differences among private-sector borrowers 2. Ignores the potential for credit risk reduction via loan diversification These potentially result in too large a capital requirement!,B

6、IS Regulatory Model Vs Credit Risk Models,Bank of Thailand,Risk Management Symposium - September 2000,Page 6,BIS Regulatory Model Vs Credit Risk Models,Big difference in probability of default exists across different credit qualities.,Note: 1. Probability of default is based on 1-year horizon. 2. Hi

7、storical statistics from Standard & Poors CreditWeek April 15, 1996.,Bank of Thailand,Risk Management Symposium - September 2000,Page 7,BIS Regulatory Model Vs Credit Risk Models,Default correlations can have significant impact on portfolio potential loss. KMV finds that correlations typically lie i

8、n the range 0.002 to 0.15.,8%,8%,BIS model requires 8% of total.,8%,Correlation = 1,Correlation = 0.15,Actual exposure is only 6% of total.,天马行空官方博客： ；QQ:1318241189；QQ群：175569632,Bank of Thailand,Risk Management Symposium - September 2000,Page 8,BIS Regulatory Model Vs Credit Risk Models,The capital

9、 requirement to cover unexpected loss decreases rapidly as the number of counterparties becomes larger.,Unexpected loss,# of counterparties,1,16,8%,3.54%,Assumption: All loans are of equal size, and correlations between different counterparties are 0.15.,Bank of Thailand,Risk Management Symposium -

10、September 2000,Page 9,Current Issues in Credit Risk Modelling,Adapted from “Credit Risk Modelling: Current Practices and Applications”, April 1999, by Basle Committee on Banking Supervision,Bank of Thailand,Risk Management Symposium - September 2000,Page 10,Current Issues in Credit Risk Modelling,Ad

11、apted from “Credit Risk Modelling: Current Practices and Applications”, April 1999, by Basle Committee on Banking Supervision,Bank of Thailand,Risk Management Symposium - September 2000,Page 11,Current Issues in Credit Risk Modelling,Adapted from “Credit Risk Modelling: Current Practices and Applica

12、tions”, April 1999, by Basle Committee on Banking Supervision,Bank of Thailand,Risk Management Symposium - September 2000,Page 12,Current Issues in Credit Risk Modelling,Adapted from “Credit Risk Modelling: Current Practices and Applications”, April 1999, by Basle Committee on Banking Supervision,Ba

13、nk of Thailand,Risk Management Symposium - September 2000,Page 13,Credit Risk Models,(A) Purpose of a credit risk model Measuring economic risk caused by Defaults Downratings Identifying risk sources and their contributions Scenario analysis and Stress test Economic capital requirement and allocatio

14、n Performance evaluation (e.g. RAROC),Bank of Thailand,Risk Management Symposium - September 2000,Page 14,Credit Risk Models,(B) Common Components 1. Model structure,Transaction 1 Transaction 2 .,Transaction 1 Transaction 2 .,Counterparty A,Counterparty B,Portfolio of several counterparties and tran

15、sactions,Correlations,Bank of Thailand,Risk Management Symposium - September 2000,Page 15,Credit Risk Models,2. Quantitative variables/parameters - Default probability/intensity (PD, EDF) - Loan equivalent exposure (LEE) - Loss given default (LGD), Recovery rate (RR), Severity (SEV) - Loss distribut

16、ion - Expected loss (EL) - Unexpected loss (UL), Portfolio risk - Economic capital (EC) - Risk contributions (RC), Contributory economic capital (CEC),Bank of Thailand,Risk Management Symposium - September 2000,Page 16,Credit Risk Models,(C) Model from Insurance (Credit Risk+) - Only two states of t

17、he world are considered- default and no default. - Spread changes (both due to market movement and rating upgrades/downgrades) are considered part of market risk. - Default probability is modeled as a continuous variable.,Bank of Thailand,Risk Management Symposium - September 2000,Page 17,Credit Ris

18、k Models,(C) Model from Insurance (Credit Risk+) There are 3 types of uncertainty: 1. Actual number of defaults given a mean default intensity 2. Mean default intensity (only in the new approach!) 3. Severity of loss,Bank of Thailand,Risk Management Symposium - September 2000,Page 18,Credit Risk Mod

19、els,(C) Model from Insurance (Credit Risk+) The whole loan portfolio can be divided into classes, each of which consists of borrowers with similar default risk. Hence, a portfolio of loans to each class of borrowers can be viewed as a uniform portfolio. - m counterparties - a uniform default probabi

20、lity of p(m),Bank of Thailand,Risk Management Symposium - September 2000,Page 19,Credit Risk Models,(C) Model from Insurance (Credit Risk+),Bank of Thailand,Risk Management Symposium - September 2000,Page 20,Credit Risk Models,(C) Model from Insurance (Credit Risk+) Within each class of counterparti

21、es, number of defaults follows Poisson Distribution.,m = number of counterparties p(m) = uniform default probability n = number of defaults in 1 year,Bank of Thailand,Risk Management Symposium - September 2000,Page 21,Credit Risk Models,(C) Model from Insurance (Credit Risk+) If default intensity (

22、) is constant, defaults are implicitly assumed to be independent (zero correlation). This is the old approach. We know that counterparties are somewhat dependent. As a result, the old approach is not realistic (too optimistic).,Bank of Thailand,Risk Management Symposium - September 2000,Page 22,Cred

23、it Risk Models,(C) Model from Insurance (Credit Risk+) The new approach incorporates dependency of counterparties by assuming that default intensity is random and follows gamma distribution.,defines shape, and defines scale of the distribution.,Default intensity,Probability density,Bank of Thailand,

24、Risk Management Symposium - September 2000,Page 23,Credit Risk Models,(C) Model from Insurance (Credit Risk+),Number of defaults (n),Default intensity ( ),Bank of Thailand,Risk Management Symposium - September 2000,Page 24,Credit Risk Models,(C) Model from Insurance (Credit Risk+) Defaults are now r

25、elated since they are exposed to the same default intensity. Higher default intensity effects all obligors in the portfolio.,First moment:,Second moment:,Mean Variance (Over-dispersion),Bank of Thailand,Risk Management Symposium - September 2000,Page 25,Credit Risk Models,(C) Model from Insurance (C

26、redit Risk+) Negative Binomial Distribution (NGD) exhibits over-dispersion and “fatter tails”, which make it closer to reality than Poisson Distribution.,# of defaults,Probability density,EL(P) = EL(NGD) UL(P) UL(NGD),Bank of Thailand,Risk Management Symposium - September 2000,Page 26,Credit Risk Mo

27、dels,(C) Model from Insurance (Credit Risk+) The last source of uncertainty is the loss amount in case of default (LEE*LGD) This is modeled by bucketing into exposure bands and identifying the probability that a defaulted obligor has a loss in a given band with the percentage of all counterparties w

28、ithin this given band.,Bank of Thailand,Risk Management Symposium - September 2000,Page 27,Credit Risk Models,(C) Model from Insurance (Credit Risk+),Probability Distribution of Loss Amount,Bank of Thailand,Risk Management Symposium - September 2000,Page 28,Credit Risk Models,(C) Model from Insuranc

29、e (Credit Risk+),Probability distribution of # of defaults,Probability distribution of loss amount,The analytic formula of the loss distribution in the form of probability generating function (PGF),Probability, EL, UL, and Percentile can be found.,Bank of Thailand,Risk Management Symposium - Septemb

30、er 2000,Page 29,Credit Risk Models,(D) Credit Metrics - Introduced in 1997 by J.P. Morgan. - Both defaults and spread changes due to rating upgrades/downgrades are incorporated. - Credit migration (including default) is discrete. - All counterparties with the same credit rating have the same probabi

31、lity of rating upgrades, rating downgrades, and defaults.,Bank of Thailand,Risk Management Symposium - September 2000,Page 30,Credit Risk Models,(D) Credit Metrics Analysis is done on each individual counterparty, which will then be combined into a portfolio, using correlations. Therefore, the only

32、key type of uncertainty modeled here is the credit rating (or default) at which a particular counterparty will be one year from now.,Bank of Thailand,Risk Management Symposium - September 2000,Page 31,Credit Risk Models,(D) Credit Metrics,Bank of Thailand,Risk Management Symposium - September 2000,P

33、age 32,Credit Risk Models,(D) Credit Metrics In the counterparty level, two inputs are required: 1. Credit transition matrix (Moodys, S&P or KMV),Source: Standard & Poors CreditWeek April 15, 1996,Bank of Thailand,Risk Management Symposium - September 2000,Page 33,Credit Risk Models,(D) Credit Metri

34、cs 2. Spread matrix and recovery rates,Source: Carty & Lieberman (96a) -Moodys Investor Service,Bank of Thailand,Risk Management Symposium - September 2000,Page 34,Credit Risk Models,(D) Credit Metrics Possible values of loan one year from now can then be calculated, each of which has its own probab

35、ility:,Now, the loan is rated BBB. Its bond equivalent yield is Rf + SBBB.,1 year,Bank of Thailand,Risk Management Symposium - September 2000,Page 35,Credit Risk Models,(D) Credit Metrics,Loss = Vcurrent - Vnew EL, UL, Percentile, and VaR can be found.,E(V),V(1st -percentile),VaR,Bank of Thailand,Ri

36、sk Management Symposium - September 2000,Page 36,Credit Risk Models,(D) Credit Metrics In the portfolio level, correlations are needed to combine all counterparties (or loans) and find the portfolio loss distribution: - “Ability to pay” = “Normalized equity value” - Migration probabilities predefine

37、 buckets (lower and upper thresholds) for the future ability to pay - Correlation of default and migrations can, hence, be derived from correlation of the “ability to pay”.,Bank of Thailand,Risk Management Symposium - September 2000,Page 37,Credit Risk Models,(D) Credit Metrics In order to find the

38、loss distribution of a 2-counterparty portfolio, we need to calculate the joint migration probabilities and the payoffs for each possible scenario:,Probability that counterparty 1 and 2 will be rated BB and BBB respectively,Bank of Thailand,Risk Management Symposium - September 2000,Page 38,Credit R

39、isk Models,(D) Credit Metrics,Sample Joint Transition Matrix(assuming 0.3 asset correlation),Source: Credit Metrics- Technical Document, April 2, 1997, p. 38,Bank of Thailand,Risk Management Symposium - September 2000,Page 39,Credit Risk Models,(D) Credit Metrics For N counterparties, one way to fin

40、d the loss distribution is to keep expanding the joint transition matrix. This, however, rapidly becomes computationally difficult (the number of possible joint transition probabilities is 8N). Another way is to sum counterparty asset volatilities is to use the variance summation equation. This is a

41、cceptable only for the loss distributions that are close to normal.,Bank of Thailand,Risk Management Symposium - September 2000,Page 40,Credit Risk Models,(D) Credit Metrics For computing the distribution of loan values in the large sample case where loan values are not normally distributed, Credit

42、Metrics uses Monte Carlo simulation. The Credit Metrics portfolio methodology can also be used for calculating the marginal risk contribution (RC) for individual counterparties. RC is useful in identifying the counterparties to which we have excessive risk exposure.,Bank of Thailand,Risk Management

43、Symposium - September 2000,Page 41,Credit Risk Models,(D) Credit Metrics,Exposure Distribution,Rating migration likelihoods,Spread matrix and recovery rates,Correlations,Joint credit rating changes,Portfolio components and market volatilities,Value and loss distribution of individual obligors,Portfo

44、lio value and loss distribution,EL, UL, Percentile, and VaR can be found.,Summary,Bank of Thailand,Risk Management Symposium - September 2000,Page 42,Credit Risk Models,(E) “KMV-Type” Model - One or both defaults and spread changes due to rating upgrades/downgrades can be incorporated. - EDF is firm

45、-specific. - EDF varies continuously with firm asset value and volatility. - Potentially a continuous credit migration.,Bank of Thailand,Risk Management Symposium - September 2000,Page 43,Credit Risk Models,(E) “KMV-Type” Model Analysis is done on each individual counterparty, which will then be com

46、bined into a portfolio, using asset-value correlations. Therefore, the only key type of uncertainty modeled here is whether or not the asset value of each firm, one year from now, will be higher than the value of its liabilities.,Bank of Thailand,Risk Management Symposium - September 2000,Page 44,Cr

47、edit Risk Models,(E) “KMV-Type” Model,Ability to pay = Asset value,Time,0,1,Default point = Value of liabilities,Asset value distribution,Default probability,Value,Bank of Thailand,Risk Management Symposium - September 2000,Page 45,Credit Risk Models,(E) “KMV-Type” Model The question is “how to find

48、 the distribution of future asset value”. KMV defines the distribution by the mean asset value and the asset volatility (or standard deviation). The question now becomes “how to find the asset value and its volatility”.,Bank of Thailand,Risk Management Symposium - September 2000,Page 46,Credit Risk

49、Models,(E) “KMV-Type” Model Since we can observe only equity value and its volatility, the link between equity and asset values and that between equity and asset volatilities need to be established. KMV solve this problem using an option pricing model.,Bank of Thailand,Risk Management Symposium - Se

50、ptember 2000,Page 47,Credit Risk Models,(E) “KMV-Type” Model,Firm value,Equity value,Book value of liabilities,Book value of liabilities,Liabilities “Short put”,Equity “Long call”,Bank of Thailand,Risk Management Symposium - September 2000,Page 48,Credit Risk Models,(E) “KMV-Type” Model Equity is li

51、ke a call option on the firm asset:,Two unknowns ( and ) can be solved from these two equations.,Bank of Thailand,Risk Management Symposium - September 2000,Page 49,Credit Risk Models,(E) “KMV-Type” Model Distance to default (DD) is then calculated:,Since the asset value distribution is not normal,

52、KMV links DD to EDF using historical relationship.,Bank of Thailand,Risk Management Symposium - September 2000,Page 50,Credit Risk Models,(E) “KMV-Type” Model KMV claims that for a given DD, EDF is remarkably constant across key variables: - Industry/sector - Company size - Time This provides a robu

53、st basis for DD-EDF mapping.,Bank of Thailand,Risk Management Symposium - September 2000,Page 51,Credit Risk Models,(E) “KMV-Type” Model Like Credit Metrics, correlations are needed to combine all counterparties (or loans) into a portfolio and find the portfolio loss distribution: - “Ability to pay”

54、 = “Market value of the firm asset” - EDF is defined as a chance that the “ability to pay” will reach the default point. - Correlation of default can, hence, be derived from correlation of asset value.,Bank of Thailand,Risk Management Symposium - September 2000,Page 52,Credit Risk Models,(E) “KMV-Type” Model For 2 co